Brady has questioned the Manchester United legend's commitment to his job at St Andrews.
In a new Amazon Prime documentary series, Brady tells confidants: "I'm a little worried about our head coach's work ethic.
"I mean, I don't know, I don't have great instincts on that."
Rooney was sacked in 2023/24 relegation season for Birmingham.
Brady makes his comments about Rooney following a visit to the club's training ground in November 2023.
The seven-time Superbowl winner also slams the players after their relegation at the end of the 2023/24 season.
"Well we've already changed the coach, so it's really the players because the coach doesn't go out there and put the ball in the goal," he says.
"They were lazy, they were entitled and when you're lazy and entitled, you don't have much of a chance to succeed.
"We've got to change all the people that are associated with losing, so I think this summer there's going to be a lot of people gone."